The model whereby a charitable organization has a non-charitable arm does exist and is seen from time to time. I would point out, however, that the non-charitable organization isn't necessarily for profit. In other words, it could be another not-for-profit organization with commercial operations aimed at fundraising for the charitable arm.
I don't bring this up to muddy the waters, but is Me to We a profit-oriented enterprise? I don't know. All I'm saying is that it's fairly rare to see a profit-oriented enterprise closely associated with a charitable organization. What is more common is a non-charitable not-for-profit organization with close ties to a charitable organization.